How do you make great looking screen recordings for SaaS demos?

I made some screen videos of some functions of our product yesterday and included them in our latest blog post highlighting some functions. It's something at least, but I'm not satisfied with the quality. I used Awesome Screenshot but the free version only offers 720p quality with webm export, and even that way the HD didn't look so good, felt like a scaled up 480p. I used gfycat to embed the video, but it feels kind of awkward when embedded: the video starts on its own and there's not much you can do against it, or at least I'm not tech savvy enough to solve this. So how do you do it? Any recommendation is welcome, free or paid tools as well!